1) The two days of Rosh Hashanah are considered like one long sanctity, and because of this the halachic authorities are in dispute as to whether on makes the blessing “Shehecheyanu” when lighting the candles, making Kiddush and blowing the shofar. Because of this, in an ideal scenario a woman should put on new clothes when lighting the candles and say the blessing and intend to use it for the new clothes, and during Kiddush they should put a new fruit on the table and use the blessing for that, and the shofar-blower should wear new clothes on the second day.
2) However, even in the case that no new fruit or clothes can be found, the blessing of “Shehecheyanu” should still be made as even though it is one long sanctity it is nevertheless two separate days, and one should make “Shehecheyanu” for the second day.